Problem: Rewrite as a simplified fraction. ${0.97\overline{5} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 975.5555...\\ 100x &= 97.5555...\end{align*}}$ Subtracting the two equations, we have: ${900x = 878}$ ${x = \dfrac{878}{900}} $ ${x = \dfrac{439}{450}} $